Racionalize $$\frac{\sqrt{2}}{\sqrt{2} + 1}$$.
Solução:
Multiplicamos o numerador e o denominador por $$\sqrt{2} – 1$$.
$$\frac{\sqrt{2}}{\sqrt{2} + 1} = \frac{\sqrt{2}}{\sqrt{2} + 1}\cdot \frac{\sqrt{2} – 1}{\sqrt{2} – 1} = $$
$$= \frac{\sqrt{2}(\sqrt{2} – 1)}{(\sqrt{2} + 1)(\sqrt{2} – 1)} = \frac{(\sqrt{2})^{2} – \sqrt{2}}{(\sqrt{2})^{2} – 1^{2}} = $$
$$= \frac{2 – \sqrt{2}}{2 – 1} = 2 – \sqrt{2}$$
